Poisson kernel of half spaces in real hyperbolic spaces

Tomasz Byczkowski (1) , Piotr Graczyk (2) , Andrzej Stos (3)

1 PWR - Institute of Mathematics
2 LAREMA - Laboratoire Angevin de Recherche en Mathématiques
3 LMBP - Laboratoire de Mathématiques Blaise Pascal

We provide an integral formula for the Poisson kernel of half-spaces for Brownian motion in real hyperbolic space $\H^n$. This enables us to find asymptotic properties of the kernel. We also show convergence to the Poisson kernel of the whole space $\H^n$. For n=3, 4 or 6 we compute explicit formulas for the Poisson kernel itself.

Mots clés: hyperbolic spaces; Brownian motion; Poisson kernel

Domaines: Probabilités [math.PR]

Tomasz Byczkowski, Piotr Graczyk, Andrzej Stos. Poisson kernel of half spaces in real hyperbolic spaces. Revista Matemática Iberoamericana, 2007, 23 (2007), no. 1, pp.85--126. ⟨hal-00079091⟩